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# Find the derivative $\frac{d}{dx}\left(\sqrt{5-x}+x+y^2\right)$ using the sum rule

## Step-by-step Solution

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###  Videos

$\frac{-1}{2\sqrt{5-x}}+1$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\sqrt{5-x}+x+y^2\right)$

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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(\sqrt{5-x}\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(y^2\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\sqrt{5-x}\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(y^2\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx((5-x)^1/2+xy^2) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (y^2) is equal to zero. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

$\frac{-1}{2\sqrt{5-x}}+1$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of ((5+-1x)^0.5+x) using the product ruleFind derivative of ((5+-1x)^0.5+x) using the quotient ruleFind derivative of ((5+-1x)^0.5+x) using logarithmic differentiationFind derivative of ((5+-1x)^0.5+x) using the definition

SnapXam A2

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Sum Rule of Differentiation

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